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Additional info for A statistical test suite for random and pseudorandom number generators for cryptographic applications (SuDoc C 13.10:800-22)
Large values would imply substantial fluctuation or irregularity. 7 Input Size Recommendation Choose m and n such that m < log2 n -2. 01, accept the sequence as random. 1 Test Purpose The focus of this test is the maximal excursion (from zero) of the random walk defined by the cumulative sum of adjusted (-1, +1) digits in the sequence. The purpose of the test is to determine whether the cumulative sum of the partial sequences occurring in the tested sequence is too large or too small relative to the expected behavior of that cumulative sum for random sequences.
0312)) 2 (0 ! 333033 (8) For each state of x, compute P-value = igamc(5/2, ! 2 ( obs ) 2 ) . Eight P-values will be produced. 333033 # , ! 502529. 01, then conclude that the sequence is non-random. Otherwise, conclude that the sequence is random. 502529), the conclusion is that the sequence is random. Note that if χ2(obs) were too large, then the sequence would have displayed a deviation from the theoretical distribution for a given state across all cycles. , n ≥ 106). 01, and the conclusion would be that the sequence was random.
077147 )2 + (1 ! 167729. 166269 2 (5) & 5 ' 2 ( obs ) # !. $2, ! 167729 # , ! 274932. 01, then conclude that the sequence is non-random. Otherwise, conclude that the sequence is random. 274932), the conclusion is that the sequence is random. 01) and 4) a conclusion of non-randomness would have resulted. , n ≥ 106). Various values of m may be selected, but for the time being, NIST recommends m = 9 or m = 10. If other values are desired, please choose these values as follows: • n ≥ MN. • N should be chosen so that N • (min πi) > 5.
A statistical test suite for random and pseudorandom number generators for cryptographic applications (SuDoc C 13.10:800-22) by U.S. National Archives and Records Administration